Clustering of data is a well-known problem of pattern recognition. For our purposes, data clustering can be formulated as follows. Given a set of data points, one looks for possible structures by sorting out which points are close to each other and, therefore, in some sense belong together. In general, data clustering is often ill-defined in a mathematical sense. Nonetheless, it is a very important problem in many scientific and technological fields of study. Data clustering is a preliminary analysis stage taken before investigating what properties are common to these subsets of the data. Some known approaches for data clustering make use of physical modeling and intuition.
One example of such an approach is known as quantum clustering (as described in US 2004/0117403 and in an article by Horn et al., “Algorithm for Data Clustering in Pattern Recognition Problems Based on Quantum Mechanics”, Phys. Rev. Lett. 88 018702 (2001), both of which are hereby incorporated by reference in their entirety). Briefly, in this approach, the data points are used to define a quantum state (e.g., this state can be composed of a linear combination of Gaussians centered at each data point). A potential function having this state as its ground state is calculated from the time-independent Schrödinger equation. The minima of this potential function provide helpful information for data clustering (e.g., in favorable cases, distinct minima of the potential function can identify the clusters). In this approach, there is a single scale parameter, which determines the scale at which cluster structures are identified.
In some cases, the performance of this quantum clustering approach can have an undesirably high sensitivity to the value of the quantum clustering scale parameter. Accordingly, it would be an advance in the art to provide data clustering having reduced parameter sensitivity. While the quantum wave function (i.e. Parzen function) can be quite sensitive to the choice of scale parameter, the details of the quantum potential are much less sensitive to this choice.